Crude pipe bombs meant for former US President Barack Obama, Hillary Clinton and CNN have been intercepted.
New York governor Andrew Cuomo said his office received a similar package and the FBI said Florida Representative Deborah Wasserman Schultz also did.
A similar device was found on Monday at the New York estate of liberal billionaire George Soros, a major contributor to Democratic causes.
There were no explosions and no reports of injuries.
The bombs were intercepted two weeks before nationwide US elections.
'These terrorising acts are despicable'
Media outside the Time Warner Building after an explosive device was delivered to CNN's New York bureau.
The White House condemned the attacks with Republican Vice President Mike Pence said they "have no place in this country", and Mr Trump tweeted "I agree wholeheartedly."
John Miller from the New York Police Department’s head of intelligence and counter-terrorism said that all the bombs seemed to come from the same person or people.
The US Secret Service intercepted a bomb that was addressed to Mrs Clinton at the home in Chappaqua, New York, she shares with former president Bill Clinton, and another that was sent to Mr Obama at his home with Michelle Obama in Washington.
A police bomb squad removed another one from CNN's New York headquarters, which was evacuated.
The package sent to CNN contained a live explosive and envelope with white powder, and officials said the substance was being tested to see if it was dangerous.
White House press secretary Sarah Sanders said in a statement: "These terrorising acts are despicable, and anyone responsible will be held accountable to the fullest extent of the law."
Two law enforcement officials said the pipe bomb at CNN was crude but operational and was addressed to former CIA director John Brennan, who regularly appears as a television contributor and who has publicly criticised Mr Trump.